Problem: Multiply the following complex numbers: $({2-2i}) \cdot ({-5i})$
Solution: Complex numbers are multiplied like any two binomials. First use the distributive property: $ ({2-2i}) \cdot ({-5i}) = $ $ ({2} \cdot {0}) + ({2} \cdot {-5}i) + ({-2}i \cdot {0}) + ({-2}i \cdot {-5}i) $ Then simplify the terms: $ (0) + (-10i) + (0i) + (10 \cdot i^2) $ Imaginary unit multiples can be grouped together. $ 0 + (-10 + 0)i + 10i^2 $ After we plug in $i^2 = -1$ , the result becomes $ 0 + (-10 + 0)i - 10 $ The result is simplified: $ (0 - 10) + (-10i) = -10-10i $